Eisenstein series attached to lattices¶and modular forms on orthogonal groups

Abstract:

We study certain vector valued Eisenstein series on the metaplectic cover of SL₂(ℝ), which transform with the Weil representation associated with the discriminant group of an even lattice L. We find a closed formula for the Fourier coefficients in terms of Dirichlet L-series and representation numbers of L modulo “bad” primes. Such Eisenstein series naturally occur in the context of Borcherds' theory of automorphic products. We indicate some applications to modular forms on the orthogonal group of L with zeros on Heegner divisors.